Question: Simplify the following expression: $p = \dfrac{-6n^2 - 60n - 96}{n + 8} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-6$ , so we can rewrite the expression: $ p =\dfrac{-6(n^2 + 10n + 16)}{n + 8} $ Then we factor the remaining polynomial: $n^2 + {10}n + {16} $ ${8} + {2} = {10}$ ${8} \times {2} = {16}$ $ (n + {8}) (n + {2}) $ This gives us a factored expression: $\dfrac{-6(n + {8}) (n + {2})}{n + 8}$ We can divide the numerator and denominator by $(n - 8)$ on condition that $n \neq -8$ Therefore $p = -6(n + 2); n \neq -8$